Abstract
We prove infinite-time extensions of invariance principles for certain random walks with essentially compact state spaces. The extensions are uniform-like in time since they use the $\bar{d}$-metric of the Bernoulli theory and imply the classical results. These are then generalized to couplings involving an isomorphism between the processes. In general a Doeblin-type condition is needed to hold for the walks but relaxation of this is indicated.
Citation
Kari Eloranta. "$\alpha$-Congruence for Markov Processes." Ann. Probab. 18 (4) 1583 - 1601, October, 1990. https://doi.org/10.1214/aop/1176990634
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